Problem: Rewrite as a simplified fraction. ${1.7\overline{2} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 172.2222...\\ 10x &= 17.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 155}$ ${x = \dfrac{155}{90}} $ ${x = \dfrac{31}{18}} \text{or} {1 \dfrac{13}{18}}$